Subgroups — C₃×#24922524 #44544409

Order 31980.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₂₆₆₅	C₂	1	1	yes	maximal, characteristic
2	#24922524	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅×C₁₃×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×#14523821	—	5	1	no	maximal, Hall
5	D₂₆₆₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅₃₃	—	5	1	no	—
7	C₅×C₁₃×C₄₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₃×#11717962	—	13	1	no	maximal, Hall
9	#14523821	—	5	1	no	Hall
10	C₃×C₁₃×C₄₁	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃×D₂₀₅	—	13	1	no	—
12	D₅₃₃	—	5	1	no	—
13	#11717962	—	13	1	no	Hall
14	C₃×#63121	—	41	1	no	maximal, Hall
15	C₃×C₅×C₄₁	#261	1	1	yes	characteristic, complemented, Hall
16	C₁₃×C₄₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
17	C₃×#4223	—	65	1	no	Hall
18	D₂₀₅	—	13	1	no	—
19	C₃×D₆₅	—	41	1	no	—
20	#63121	—	41	1	no	Hall
21	C₃×D₄₁	—	65	1	no	—
22	C₅×C₄₁	C₃×#261	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅×C₁₃	#4223	1	1	yes	characteristic, complemented, Hall
24	#4223	—	65	1	no	Hall
25	C₃×#261	—	205	1	no	Hall
26	D₆₅	—	41	1	no	—
27	C₃×C₄₁	#63121	1	1	yes	characteristic, complemented, Hall
28	D₄₁	—	65	1	no	—
29	C₃×D₁₃	—	205	1	no	—
30	C₅×C₁₃	C₃×#4223	1	1	yes	characteristic, complemented, Hall
31	C₃×AGL(1,𝔽₅)	—	533	1	no	Hall
32	#261	—	205	1	no	Hall
33	C₄₁	C₃×#63121	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₁₃	#11717962	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	—	533	1	no	—
36	D₁₃	—	205	1	no	—
37	AGL(1,𝔽₅)	—	533	1	no	Hall
38	C₃×C₅	#14523821	1	1	yes	characteristic, complemented, Hall
39	C₁₃	C₃×#11717962	1	1	yes	characteristic, complemented, Sylow
40	C₃×C₄	—	2665	1	no	Hall
41	D₅	—	533	1	no	—
42	C₂×C₃	—	2665	1	no	—
43	C₅	C₃×#14523821	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	2665	1	no	Sylow
45	C₃	#24922524	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	—	2665	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#24922524
commutator, hypocenter	C₅×C₁₃×C₄₁	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₄₁	C₄
prime radical	C₃×D₂₆₆₅	C₂
cosocle	D₂₆₆₅	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₄₁
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #24922524	C₃	direct (N × H)
3. C₃×C₅×C₁₃×C₄₁	C₄	semidirect
7. C₅×C₁₃×C₄₁	C₃×C₄	semidirect
10. C₃×C₁₃×C₄₁	AGL(1,𝔽₅)	semidirect
15. C₃×C₅×C₄₁	#261	semidirect
16. C₁₃×C₄₁	C₃×AGL(1,𝔽₅)	semidirect
22. C₅×C₄₁	C₃×#261	semidirect
23. C₃×C₅×C₁₃	#4223	semidirect
27. C₃×C₄₁	#63121	semidirect
30. C₅×C₁₃	C₃×#4223	semidirect
33. C₄₁	C₃×#63121	semidirect
34. C₃×C₁₃	#11717962	semidirect
38. C₃×C₅	#14523821	semidirect
39. C₁₃	C₃×#11717962	semidirect
43. C₅	C₃×#14523821	semidirect
45. C₃	#24922524	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₂₆₆₅	2
#24922524	3
C₃×#14523821	5
C₃×#11717962	13
C₃×#63121	41

Subgroups — C3×#24922524 #44544409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#24922524 #44544409